It could be possible that Mr. Dark is Dark Rayman & Raymesis' father, due to the fact that Mr. Dark created this clone. It is unknown if Rayman and Raymesis are siblings in general, however.
In Rayman, he appeared on the second level of Candy Chateau after Mr Dark summons him, where he would copy every move Rayman made. If he touched Rayman, he would kill him instantly (He would also die). He could be defeated by reaching the exit before he did, which would cause him to collapse and die. It is possible however to do the entire level without having to worry about him chasing you. In order to accomplish this, the player would merely need to jump over the activation spark at the start of the level, preventing Dark Rayman from spawning at all- however this is only possible in the Playstation version. ( All of this however is before he is created again with a new appearance & new name as The name "Dark Rayman" is later taken by the separated being that became the dark force as first seen in Rayman Legends)
In Rayman 1 for the Gameboy Color, he appeared on the third level of the Arcane Forest, where he would do exactly the same thing. There was a rare glitch which caused him to disappear if he was too far off-screen. Dark Rayman (now reborn as Raymesis) has a different appearance though. His skin color was brown, he has purple hair, golden shoes and gloves, and a purple neckerchief and shirt with the "O" on it, but sometimes makes it a lighter purple.
In Rayman Arena, his appearance was much different. He had red eyes, matching gloves, and hair (or yellow-ish blonde or orange-ish blonde), orange shoes with white areas one of them a shoe strap on top, and a black shirt (looks mostly a dark grape purple or violet), with an white X on it. He is the main antagonist of the game and appears as the enemy in all of the bonus levels.
His character is first established in the Master League, where the player must defeat him in all modes of the game. Once he was defeated, he'd become a playable character.
When Raymesis speaks to the Bubble Dreamer, he makes fun of his ugliness, and blames that on Mr. Dark from the first game. This is the first video game to allow Raymesis to be playable. Raymesis never appeared as the main villain (or even a minor one) in the game, and didn't copy Rayman.
Raymesis appears in Legends seems to have turned to "The Elec Side". He is a playable character , but in certain Invaded levels, players will have to deal with Dark Rayman (the being that was separated from Raymesis in Candy Chateau & became it's own dark force that continued to follow it's original propose) following them and mimicking their every move, forcing them to keep moving. Touching him means instant death again as well. He functions very similarly to his first appearance. In this particular incarnation, he is completely blacked out, with only glowing yellow eyes. If there are more than one players, Dark Rayman will copy the leading player's movements. Raymesis himself remains a hero.
He is also an unlockable character as he was in Origins, retaining his appearance from said game. He is called "Raymesis" here aswell.